Details

sample39.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.3s

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

145.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
549.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
794.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
536.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
213.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
200.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.0s

Counts: 477 → 477

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
58×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
53×	`times-frac`
38×	`add-cube-cbrt` `add-cbrt-cube`
28×	`div-exp`
18×	`associate-l`
16×	`prod-exp`
15×	`cbrt-undiv` `associate-r`
10×	`associate-/r*` `associate-/r/`
9×	`distribute-lft-out`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
5×	`rec-exp` `1-exp` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 171

Calls

4 calls:

61.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
482.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
651.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
368.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
243.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
214.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
129.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.4s

Counts: 183 → 183

prune510.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

819×	`times-frac`
601×	`*-un-lft-identity`
360×	`sqrt-prod`
355×	`add-sqr-sqrt`
349×	`add-cube-cbrt`
126×	`distribute-lft-out`
71×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
2×	`sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 477

Calls

4 calls:

316.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
717.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
406.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
341.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
176.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
119.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.6s

Counts: 489 → 489

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize39.0ms

Local error

Found 4 expressions with local error:

2.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.0b	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (/ (sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
11.0b	(sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

1276×	`times-frac`
841×	`sqrt-prod`
757×	`*-un-lft-identity`
684×	`add-sqr-sqrt`
515×	`add-cube-cbrt`
402×	`associate-r`
116×	`distribute-lft-out`
78×	`associate-/r/`
41×	`flip3-+` `flip-+`
39×	`div-inv`
36×	`unswap-sqr`
33×	`associate-l`
17×	`sqrt-div`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-/l*`
7×	`rem-sqrt-square` `sqrt-pow1`
4×	`associate-/l/` `add-log-exp` `pow-div`
3×	`cbrt-undiv` `pow1/2` `div-exp`
2×	`pow-flip` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `inv-pow`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 689

Calls

4 calls:

401.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
344.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.4s	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (/ (sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
118.0ms	(sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
123.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
182.0ms	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (/ (sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
224.0ms	(sqrt (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify1.7s

Counts: 701 → 701

prune4.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.6b

regimes117.0ms

Accuracy

31.1% (1.8b remaining)

Error of 2.9b against oracle of 1.1b and baseline of 3.7b

bsearch152.0ms

Steps

Iters	Range		Point
9	8.066893326501095e+49	2.5763926787028215e+55	1.7901443844279982e+55

simplify1.2s

end0.0ms

sample1.7s

Algorithm

intervals

Results

701.0ms	8000×	body	80	valid
634.0ms	8000×	pre	80	true